I've just had my first flat. Luckily, it happened right in front of my building. The tire is coming off the rim already. Does that signify anything? Also, if I decide to take the bike to the DIY bike workshop tomorrow, will rolling it on a flat tire cause harm?

I want to go to the workshop because I have a brake problem I don't know how to fix, and I might as well fix the flat there too. I live in Manhattan so transporting my bike by car isn't an option (unless I pay a car service which is pricey).

Thanks for any advice.

Pam